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Let A = [–1, 1]. discuss whether the following functions defined on A are one-one, onto or bijective: g(x) = |x|

Let A = [–1, 1].  
 discuss whether the following functions defined on A are one-one, onto or bijective: 
  g(x) = |x| 
 

Grade:12

1 Answers

Anand Kumar Pandey
askIITians Faculty 5733 Points
5 months ago
Dear Student

g (x) = |x|
Let g (x1) = g (x2)
|x1| = |x2|
x1= ± x2
Thus, g (x) is not one-one
now g (x) = |x|≥ 0, for all real x
Hence, the range is [0, 1],
which is subset of co-domain ‘A’
Thus, f (x) is not onto.
Therefore, f (x) is not bijective.

Thanks

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